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In a small signal model we define a transient resistance. This resistance denotes the amount of change of current per differential change in voltage. One can easily notice from a standard $I-V$ characteristic curve for a diode that this resistance decreases with increasing voltage. I am unable to realize this physically, i.e. what process, which was initially offering resistance to the incoming current, is reducing?

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The current in an ideal pn-junction increases exponentially with applied forward voltage. This is due to the exponential increase of injected electron and hole (minority carrier) densities into the p- and n-regions produced by the reduction of the potential barrier across the depletion zone by the applied forward voltage. These carrier densities increase exponentially with decreasing potential energy barrier of the electrostatic field across the depletion region according to the Boltzmann energy distribution. The exponential increase of current I with applied forward bias V in the pn-junction yields by differentiation also an exponential increase of the differential conductance dI/dV of the pn-junction. Therefore the differential resistance dV/dI decreases exponentially with applied voltage V. This behavior of the pn-junction is due to the reduction of the potential barrier in the depletion zone (which prevents current flow when no voltage is applied) with applied forward voltage.

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The differential resistance of a diode, dV/dI, is a function of V (or I).

The process behind this is the thinning of the so-called depletion region in the diode. The depletion region is a layer between the P and N bulk materials in which the holes from the P material have diffused into the N, and the electrons from the N have diffused into the P, and in this depletion region there are nearly NO carriers of either sort. Applying a forward voltage moves N and P carriers toward the depletion region.

Depletion region thickness goes up with reverse bias, down with forward bias (and this is how voltage-variable-capacitance diodes operate). It never quite goes to zero (which, if it did occur, would mean the diode becomes a resistor).

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